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3 years ago

6(4x+5)=3(x+8)+3 round to the nearest hundredth

Mathematics

1 answer:

My name is Ann [436]3 years ago

8 0

Answer:

x = -0.14

Step-by-step explanation:

Given that:

6(4x+5)=3(x+8)+3

By simplifying:

24x + 30 = 3x + 24 +3

Taking terms with x to left side and others on right side

Sign will be changed when transferring term from one side to other

24x - 3x= 24 + 3 -30

21x = 27 - 30

21x = -3

x= -3/21

x= - 0.142857...

By rounding off to nearest hundredth

As the third decimal place (2) is smaller than 5
Previous digit will remain same so,

x = -0.14

I hope it will help you!

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A toy manufacturer wants to know how many new toys children buy each year. A sample of 305 children was taken to study their pur

Harrizon [31]

Answer:

The 80% confidence interval for the mean number of toys purchased each year is between 7.5 and 7.7 toys.

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1 - 0.8}{2} = 0.1$

Now, we have to find z in the Ztable as such z has a pvalue of $1 - \alpha$ .

That is z with a pvalue of $1 - 0.1 = 0.9$ , so Z = 1.28.

Now, find the margin of error M as such

$M = z\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

$M = 1.28\frac{1.5}{\sqrt{305}} = 0.1$

The lower end of the interval is the sample mean subtracted by M. So it is 7.6 - 0.1 = 7.5

The upper end of the interval is the sample mean added to M. So it is 7.6 + 0.1 = 7.7

The 80% confidence interval for the mean number of toys purchased each year is between 7.5 and 7.7 toys.

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